Humans couldn't chase or wear down much more than a chicken in their back yard.
There's a story, though I won't vouch for its complete accuracy, that a reporter was incredulous of Louis Leakey's claim that wearing down game was how early hominids hunted. They were at Leakey's camp, and Leakey was over 60 years old at the time.
Leakey took a cobble, smashed in on another to make a handax, and took off at a trot after an antelope. The antelope sprinted away, then rested, sprinted, rested..... while Leakey trotted after it. When it couldn't sprint any more - less than fifteen minutes - Leakey cracked its skull with his handax and carried it back to camp. And then skinned it with stone tools.
I, personally, might be able to hit one with the car......